{"paper":{"title":"Global hypoellipticity of the Kohn-Laplacian $\\Box_b$ on pseudoconvex CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Tran Vu Khanh","submitted_at":"2010-12-29T10:39:03Z","abstract_excerpt":"Let $X$ be a complex manifold and $M\\subset X$ a compact, smooth, pseudoconvex CR manifold of dimension $2n-1$. (Here $n\\ge 3$ or, in case $n=2$, it is made the extra assumption that $\\dib_b$ has closed range on functions.) Assume that there exists a strictly CR-plurisubharmonic function in a neighborhood of $M$ in $X$. In this situation, there are here proved \\begin{enumerate}\n  \\item[(i)] The global existence of $C^\\infty$ solutions to the tangential Cauchy-Riemann operator $\\dib_b$.\n  \\item[(ii)] The global hypoellipticity of the Kohn-Laplacian $\\Box_b$, under the additional condition of \"w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5906","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}